This invention relates to the generation of electric power, and specifically to direct power generation by inducing a Faraday voltage in a propagating detonation wave. In particular, the invention concerns a combustor/coil assembly for direct Faraday induction from magnetohydrodynamic (MHD) interactions between a detonation wave and an applied magnetic field.
Electric generators traditionally require three elements: a source of magnetic field, a Faraday loop or induction coil, and an engine or other source of mechanical energy to rotate the loop with respect to the field (alternatively, to rotate the field source with respect to the loop). Relative motion of the loop and coil results in a time rate of change in the magnetic flux. The changing magnetic flux results in an induced voltage or EMF (electromotive force), which can be used to drive current through a load.
The induced EMF is determined from Faraday's law:
                                          ∫            C                    ⁢                      E            ·                          ⅆ              l                                      =                              -                          ⅆ                              ⅆ                t                                              ⁢                                    ∫              S                        ⁢                          B              ·                                                ⅆ                  A                                .                                                                        [        1        ]            In EQ. 1, the left-hand integral is a closed-contour integral of the induced electric field E over Faraday loop l. This gives the EMF, or induced voltage V. The right-hand integral is performed over any surface A bounded by the Faraday loop (l), and gives the total magnetic flux through the loop (Φ).
Faraday's law relates the induced EMF to the time rate of change in the magnetic flux through the loop; that is,
                    V        =                  -                                                    ⅆ                Φ                                            ⅆ                t                                      .                                              [        2        ]            The induced voltage (V) depends upon the strength of the magnetic field, and the geometry, orientation, and relative motion of the Faraday loop with respect to the field.
Magnetic field sources typically employ a combination of permanent magnets and field coils to generate the magnetic field. Permanent magnets are characterized by intrinsic magnetic fields, while field coils (or electromagnets) generate the magnetic field in response to an energizing current.
In one configuration the energizing current is fixed (or only permanent magnets used), so that the field is substantially constant in time. In this configuration, the flux (Φ) varies sinusoidally in time, reflecting the rotating orientation of the coil with respect to the field. The result is a sinusoidal induced voltage, which characterizes an alternating current or AC electric power generator. In the simplest power generation geometry, the alternating frequency is determined by the rotational frequency of the coil, which is typically regulated to approximately 3,000 rpm or 3,600 rpm, in order to generate AC power with a standard frequency of fifty hertz (50 Hz) or sixty hertz (60 Hz).
In other configurations the energizing current also varies in time. In these configurations the generated power is either AC power or DC power, depending upon the relative phase of the energizing current and the rotation. In some of these configurations, for example, a commutator is used to generate DC electrical power. In others, multiple-phase coils are utilized to generate three-phase power or other, more general power waveforms.
The power delivered by the generator depends upon the load, which determines the current. The current is given by Ohm's law:V=IZ,  [3]where Z is the impedance. For simple resistive loads Z=R, where resistance R has scalar form and current I is in phase with voltage V. In the more general case impedance Z has a complex phasor form to account for capacitive and inductive reactance, and the voltage and current are out of phase. In this generalized case, the average power output is=IV cos φ,  [4]where power factor φ accounts for the difference in phase (equivalently, the instantaneous power is averaged over a number of cycles).
Industrial generators and generators for aviation applications are typically powered by gas turbine engines. A gas turbine engine includes a compressor, a combustor, and a turbine, arranged in flow series with an upstream inlet and a downstream exhaust system. The compressor performs as a supercharger for the combustor, where the compressed air is mixed with fuel and ignited. Hot combustion gases exit the combustor into the turbine, where mechanical energy is extracted via a shaft which drives the compressor and a generator or other mechanical load.
Modern gas turbine engines are reliable, efficient sources of mechanical energy. They are also complex systems, with a large number of service-limited wear parts. The gas turbine engine's relatively large size and weight envelope is also a concern, particularly in aviation and aerospace applications. The result is a constant tradeoff among efficiency, weight, and reliability.
The thermodynamic efficiency of a gas turbine engine (or any engine) is limited by entropy considerations, as embodied in the Second Law of Thermodynamics. Specifically, the thermodynamic efficiency (η) is limited by
                              η          ≤                                                    T                H                            -                              T                L                                                    T              H                                      ,                            [        5        ]            where TH is the (relatively high) temperature at which energy is extracted from the combustion gas, and TL is the (relatively low) temperature of the exhaust. Because exhaust temperature TL is limited by ambient environmental conditions, improving the thermodynamic efficiency requires increasing combustion temperature TH. This in turn increases the thermal load on service-limited parts, particularly in the combustor and turbine sections.
Gains in traditional turbine-based generator efficiency are thus typically offset by reductions in service life, or require heavier, more durable parts, which increase the weight and size envelope. There remains, therefore, an ongoing need for thermodynamically efficient electric generator systems with relatively fewer service-limited wear parts, lower weight and size requirements, and adaptability to both ground-based and aviation/aerospace applications.